Which savings account should I open if I want to close my POSBkids account?

Standard Chartered JumpStart is a good pick for allowance crediting and spending since there is a 1% cashback feature. You can back it up with a Singlife account, parking any excess funds you have inside to get that sweet 2.5% p.a returns.

1) Keep up to 6 months of your expenses in a high interest saving account, such as SingLife for 2.5% interest per annum. (Emergency funds)

2) Keep maybe 10% of your savings in your ePOSBKids account. (This is for you to spend, credit your income to)

3) The rest will be fully invested in equities. (Stocks)

I would recommend DCA using Index Funds and learning how to pick your own stocks.